This paper presents a counterexample for the open conjecture whether innermost joinability of all critical pairs ensures confluence of innermost terminating term rewriting systems. We then show that innermost joinability of all normalized …

In this note, we employ the techniques of Swan (Pac J Math 12(3):1099–1106, 1962) with the purpose of studying the parity of the number of the irreducible factors of the penatomial $$X^n+X^{3s}+X^{2s}+X^{s}+1\in \mathbb {F}_2[X]$$ X n + X 3 s + X …